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A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.

%I A080155 #13 Apr 12 2014 02:24:19
%S A080155 2,3,11,31,47,229,251,577,857,859,911,1123,1223,1297,1571,2161,2417,
%T A080155 2551,2879,3319,5273,6121,6947,7603,8273,12721,12953,13291,15683,
%U A080155 16453,17207,18133,20399,23743,23909,25849,28277,28879,35291,35461,36107,43573
%N A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.
%C A080155 See A073640 for the sequence involving concatenation of 2 successive terms, A080153 for 3 successive terms. Primeness is established using Maple's isprime() function, so later terms should be regarded as "probable".
%H A080155 T. D. Noe, <a href="/A080155/b080155.txt">Table of n, a(n) for n = 1..201</a>
%F A080155 For any n>1, a(n) is prime and a(n) > a(n-1). a(n) is the smallest prime for which a(1)//a(2)//...//a(n) is prime. // denotes concatenation.
%e A080155 E.g. a(5)=47 since this is the smallest prime>a(4) which, when concatenated with the concatenation of a(1) to a(4) (=231131), also yields a prime, in this case 23113147.
%p A080155 with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: pout;
%t A080155 f[s_List] := Block[{p=NextPrime@s[[-1]], pp=FromDigits@Flatten[IntegerDigits/@s]}, While[!PrimeQ[pp*10^Floor[Log[10,p]+1]+p], p=NextPrime@p]; Append[s,p]]; Nest[f,{2},40]
%Y A080155 Cf. A073640, A080152, A080153, A080154, A080156.
%Y A080155 Cf. A033679, A069603, A074338.
%K A080155 nonn,base
%O A080155 1,1
%A A080155 Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003